#1: Yes, the download counter increments every time someone clicks 'Play', even if the player already has the D-Mod 'installed' in the browser.

#2: Maybe; other browsers are likely supported, but the newer browsers generally work better for things like this. I'd hate to 'hide' the Play button for browsers that work that I don't know about. For example, I just tried playing using Microsoft Edge (which I've never intentionally used before), and it worked great, and I was able to browse for and install a D-Mod.